PYTHAGORUS

MALINI R

1181724BD036

BACHELOR OF EDUCATION

SECOND YEAR

MATHEMATICS

MARUTHI COLLEGE OF EDUCATION

MANIVIZHUNDHAN SOUTH

2024-2026

PYTHAGORUS

INTRODUCTION

Pythagoras of Samos (Ancient Greek: Πυθαγόρας; c. 570 – c. 495 BC). was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Modern scholars disagree regarding Pythagoras's education and influences, but most agree that he travelled to Croton in southern Italy around 530 BC, where he founded a school in which initiates were allegedly sworn to secrecy and lived a communal, ascetic lifestyle.

NUMEROLOGY

Another belief attributed to Pythagoras was that of the "harmony of the spheres",which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony.According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together.

LEGENDS

Within his own lifetime, Pythagoras was already the subject of elaborate hagiographic legends. Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure. In a fragment, Aristotle writes that Pythagoras had a golden thigh, which he publicly exhibited at the Olympic Games and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo".Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications. He was supposedly once seen at both Metapontum and Croton at the same time. When Pythagoras crossed the river Kosas (the modern-day Basento), "several witnesses" reported that they heard it greet him by name. In Roman times, a legend claimed that Pythagoras was the son of Apollo.

Pythagoras was said to have dressed all in white. He is also said to have borne a golden wreath atop his head and to have worn trousers after the fashion of the Thracians. Pythagoras was said to have had extraordinary success in dealing with animals. A fragment from Aristotle records that, when a deadly snake bit Pythagoras, he bit it back and killed it. Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat fava beans and that he once convinced a notoriously destructive bear to swear that it would never harm a living thing again, and that the bear kept its word. Riedweg suggests that Pythagoras may have personally encouraged these legends, but Gregory states that there is no direct evidence of this.

ATTRIBUTED DISCOVERIES

IN MATHEMATICS

Diagram illustrating the Pythagorean theorem

The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).

Although Pythagoras is most famous today for his alleged mathematical discoveries, classical historians dispute whether he himself ever actually made any significant contributions to the field. Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem, as well as discoveries in the fields of music, astronomy, and medicine. Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides" —that is,

a2+b2=c2

{\displaystyle a^{2}+b^{2}=c^{2}}. According to a popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole hecatomb, to the gods. Cicero rejected this story as spurious[160] because of the much more widely held belief that Pythagoras forbade blood sacrifices.

IN MUSIC

According to legend, Pythagoras discovered that musical notes could be translated into mathematical equations when he passed blacksmiths at work one day and heard the sound of their hammers clanging against the anvils. Thinking that the sounds of the hammers were beautiful and harmonious, except for one, he rushed into the blacksmith shop and began testing the hammers. He then realized that the tune played when the hammer struck was directly proportional to the size of the hammer and therefore concluded that music was mathematical.

IN ASTRONOMY

In ancient times, Pythagoras and his contemporary Parmenides of Elea were both credited with having been the first to teach that the Earth was spherical, the first to divide the globe into five climatic zones, and the first to identify the morning star and the evening star as the same celestial object (now known as Venus). Of the two philosophers, Parmenides has a much stronger claim to having been the first and the attribution of these discoveries to Pythagoras seems to have possibly originated from a pseudepigraphal poem. Empedocles, who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical. By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals.

LATER INFLUENCE IN ANTIQUITY

ON GREEK PHILOSOPHY

Sizeable Pythagorean communities existed in Magna Graecia, Phlius, and Thebes during the early fourth century BC. Around the same time, the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia. According to later tradition, Archytas was elected as strategos ("general") seven times, even though others were prohibited from serving more than a year. Archytas was also a renowned mathematician and musician. He was a close friend of Plato and he is quoted in Plato's Republic. Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans. Cicero repeats this statement, remarking that Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean"). According to Charles H. Kahn, Plato's middle dialogues, including Meno, Phaedo, and The Republic, have a strong "Pythagorean coloring", and his last few dialogues (particularly Philebus and Timaeus) are extremely Pythagorean in character.

The poet Heraclitus of Ephesus (fl. c. 500 BC), who was born a few miles across the sea from Samos and may have lived within Pythagoras's lifetime,[186] mocked Pythagoras as a clever charlatan,[7][186] remarking that "Pythagoras, son of Mnesarchus, practiced inquiry more than any other man, and selecting from these writings he manufactured a wisdom for himself—much learning, artful knavery." Alcmaeon of Croton (fl. c. 450 BC), a doctor who lived in Croton at around the same time Pythagoras lived there,[71] incorporates many Pythagorean teachings into his writings and alludes to having possibly known Pythagoras personally. The Greek poets Ion of Chios (c. 480 – c. 421 BC) and Empedocles of Acragas (c. 493 – c. 432 BC) both express admiration for Pythagoras in their poems.

According to R. M. Hare, Plato's Republic may be partially based on the "tightly organised community of like-minded thinkers" established by Pythagoras at Croton.[189] Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are a secure basis for philosophy, science, and morality.[189] Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world"[189] and both were probably influenced by Orphism.[189] The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans.

IN EARLY CHRISTIONITY

Many early Christians had a deep respect for Pythagoras.[211] Eusebius (c. 260 – c. 340 AD), bishop of Caesarea, praises Pythagoras in his Against Hierokles for his rule of silence, his frugality, his "extraordinary" morality, and his wise teachings.[212] In another work, Eusebius compares Pythagoras to Moses.[212] In one of his letters, the Church Father Jerome (c. 347 – c. 420 AD) praises Pythagoras for his wisdom[212] and, in another letter, he credits Pythagoras for his belief in the immortality of the soul, which he suggests Christians inherited from him.[213] Augustine of Hippo (354–430 AD) rejected Pythagoras's teaching of metempsychosis without explicitly naming him, but otherwise expressed admiration for him.[214] In On the Trinity, Augustine lauds the fact that Pythagoras was humble enough to call himself a philosophos or "lover of wisdom" rather than a "sage".[215] In another passage, Augustine defends Pythagoras's reputation, arguing that Pythagoras certainly never taught the doctrine of metempsychosis.[215]

INFLUENCE AFTER ANTIQUITY

IN THE MIDDLE AGES

Medieval carving of a man with long hair and a long beard hunched over a musical instrument he is working

Pythagoras appears in a relief sculpture on one of the archivolts over the right door of the west portal at Chartres Cathedral.

During the Middle Ages, Pythagoras was revered as the founder of mathematics and music, two of the Seven Liberal Arts. He appears in numerous medieval depictions, in illuminated manuscripts and in the relief sculptures on the portal of the Cathedral of Chartres. The Timaeus was the only dialogue of Plato to survive in Latin translation in western Europe, which led William of Conches (c. 1080–1160) to declare that Plato was Pythagorean. In the 1430s, the Camaldolese friar Ambrose Traversari translated Diogenes Laërtius's Lives and Opinions of Eminent Philosophers from Greek into Latin and, in the 1460s, the philosopher Marsilio Ficino translated Porphyry and Iamblichus's Lives of Pythagoras into Latin as well, thereby allowing them to be read and studied by western scholars. In 1494, the Greek Neopythagorean scholar Constantine Lascaris published The Golden Verses of Pythagoras, translated into Latin, with a printed edition of his Grammatica, thereby bringing them to a widespread audience. In 1499, he published the first Renaissance biography of Pythagoras in his work Vitae illustrium philosophorum siculorum et calabrorum, issued in Messina.

LIST OF THINGS NAMED AFTER PYTHAGORUS

Ex pede Herculem, "from his foot, [we can measure] Hercules" – a maxim based on the apocryphal story that Pythagoras estimated Hercules's stature based on the length of a racecourse at Pisae

Pythagorean cup – a prank cup with a hidden siphon built in, attributed to Pythagoras

Pythagorean means – the arithmetic mean, the geometric mean, and the harmonic mean, claimed to have been studied by Pythagoras.

CONCLUSION

Pythagoras's emphasis on dedication and asceticism are credited with aiding in Croton's decisive victory over the neighboring colony of Sybaris in 510 BC. After the victory, some prominent citizens of Croton proposed a democratic constitution, which the Pythagoreans rejected. The supporters of democracy, headed by Cylon and Ninon, the former of whom is said to have been irritated by his exclusion from Pythagoras's brotherhood, roused the populace against them. Followers of Cylon and Ninon attacked the Pythagoreans during one of their meetings, either in the house of Milo or in some other meeting-place. Accounts of the attack are often contradictory and many probably confused it with the later anti-Pythagorean rebellions, such as the one in Metapontum in 454 BC. The building was apparently set on fire, and many of the assembled members perished; only the younger and more active members managed to escape.

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